If you're going in the first time not knowing exactly where to go, what buttons to push and what paths to follow, you're going to need one hell of a lot.
If you're like me, and you went in thinking "Oh look, a Vault! This will be fun!" armed with nothing but combat armor and a 10mm SMG, you're going to need to make a lot of trips. I made about three or four initial trips into the Vault, killing off all the ghouls I could and trying to understand the layout in my head. Once my rad level was too high I would pop back to a doctor and get patched up. Not the best way to do it, but I do feel like I got a better grip of the layout of the place than I would have if I was just wandering around aimlessly scratching my head, popping Rad-Away every three minutes.
lol, this is what i did,in hardcoe mode. my advice to my friends that aren't doing it in hardcoe mode is: get a radiation suit, 10 rad-x's, 10 radaways, 12 super-stims, @ 20 regular stims, some cateye and a coupla 10mm guns(all the ghouls drop 10 mm ammo), but don't take too much 'stuff' with you, cuz you'll have a bunch of booty to carry out when its all said and done